Express this quotient in scientific notation: ${\frac{4.350\times 10^{11}} {5.0\times 10^{5}}}$
Solution: Start by collecting like terms together. $= {\frac{4.350} {5.0}} \times{\frac{10^{11}} {10^{5}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.87 \times 10^{11\,-\,5}$ $= 0.87 \times 10^{6}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.87$ is the same as $8.70 \div 10$ , or $8.70 \times 10^{-1}$ $ = {8.70 \times 10^{-1}} \times 10^{6} $ $= 8.70\times 10^{5}$